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Windows Presentation Foundation Masterclass

BestsellerCreated by Tim Buchalka’s Learn Programming Academy, Eduardo RosasLast updated 10/2019EnglishEnglish Subs [Auto-generated]This course includes

  • 20 hours on-demand video
  • 1 article
  • 1 downloadable resource
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion

What you’ll learn

  • Be able to build desktop apps that leverage WPF
  • Be able to create your own cloud services
  • Learn languages and patterns that open up opportunities to create iOS, Android and UWP applications using Xamarin
  • Learn to better structure your code for easier maintenance, better code reuse, and greater compatibility with other projects (such as Xamarin and UWP)
  • Build your own app from start to finish including its cloud services such as databases and file storage

Course contentall 135 lectures 20:12:08Requirements

  • Some previous programming experience in C# or a similar language like Java is recommended, but not essential
  • Access to a computer running Windows (previously Windows 10, but Windows 7 or 8 is ok as well).
  • If not running Windows natively, a Virtual machine running Windows is required.

Description

Do you know a little programming in C# or another language, but are struggling to get an interview, let alone a job?

Maybe you are stuck in a low paying programming job, and want to move up to a better, more senior position.

Perhaps you want to learn a new skill and expand your rèsumè.

Or maybe you want to improve your .NET skills by learning a new and valuable framework.

If one or more of these things describe you, then I’d suggest you give serious consideration to this course.

This course will teach you how to create applications that have a rich user interface, using Microsoft’s Windows Presentation Foundation (WPF).

What is WPF ?

WPF is part of the .NET framework and  provides a consistent programming model for building applications by separating the user interface from business logic.  It uses XAML (an XML based language) and C#.  The runtime libraries are included with all versions of Microsoft Windows since Windows Vista.  It’s heavily supported by Microsoft and is a mature and powerful framework.

Why should you bother to learn it?

Many, perhaps most enterprise level .NET applications are built in WPF because of it’s ability to create loosely coupled apps where the business logic and presentation layer are separated.  This also applies to apps in general that are developed in .NET.  A good portion of Winforms based projects are being upgraded to WPF as well.

WPF developers are in high demand and WPF is fully supported by Microsoft in the latest versions of Visual studio and .NET.  It’s a key part of Microsoft’s strategy moving forward.

What will you learn in this course?

WPF is developed using C# and XAML.  You will learn how to use WPF to build and access powerful REST services (specifically weather information and machine learning in this course).  You will also learn to create your own cloud services, and learn languages and patterns the open up future opportunities in Xamarin as well (iOS, Android and the Universal Windows Platform (UWP).

In addition, in this course you will learn C#, XAML, the MVVM (Model-View-ViewModel) architectural pattern, Azure App and Storage services, and SQLite and more.

Why enrolling in this course is the best decision you can make.

Other courses focus on isolated examples on what you can do with WPF.  Not this course!  This course guides you through the creation of real world applications as you learn more and more about WPF. You will:

  1. Build a calculator as you learn:
    1. C#
    2. XAML
    3. Styles
  2. Build a contacts app as you learn:
    1. SQLite
    2. Using ListViews
    3. Creating Custom Controls
  3. Build a machine learning classifier as you learn:
    1. REST services
    2. Picking images from the computer
  4. Build a weather app as you learn:
    1. The MVVM architectural pattern
    2. More REST
  5. Build a notes app as you learn:
    1. More WPF controls such as toolbar, speech to text, toggle buttons, comboboxes, context menus and rich text format editors
    2. To add Azure App Services for cloud hosted databases
    3. To add Azure Storage Account services for storing files in the cloud
    4. To add Animations

Your instructor, Eduardo Rosas, is a certified Xamarin Mobile Developer who has been building apps with C# and XAML since 2012.

This means you are learning from someone who has all the professional training, skills, and experience you need to teach you how to become proficient with WPF in the fastest possible way.  But all the while being taught the right way to program.

If you are ready to get that first paid programming job, or to move up to a more senior programming position, then this course is for you!

After completing this course, you will have the necessary skills to be able to use create your own WPF desktop apps giving you increase career opportunities.

The sooner you sign up for this course, the sooner you will have the skills and knowledge you need to increase your job or consulting opportunities.    Your new job or consulting opportunity awaits!

Why not get started today?

Click the Signup button to sign up for the course!Who this course is for:

  • Anyone wanting to understand and use Windows Presentation Foundation (WPF)
  • Anyone wanting to increase career options by learning an important Microsoft Windows development technology.

Size: 3.97 GB

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Jorgen is 75 years old and was diagnosed with a life-threatening condition. he often thinks about his homeland sweden. his memories lead him to verbalize his desire to get better and visit sweden one last time before he dies. he states, if only i could visit sweden, then i would be good for the rest of my life. this would be an example of which kubler-ross stage of death and dying?


Answered by answersmine AT 22/10/2019 – 02:35 AM

The Kubler Ross Model is usually experienced by people who lost their loved ones or people who are close to death because of a terminal illness or other related circumstances. The stage of Kubler Ross Model that is being shown above is the bargaining stage. It is where an individual tries to negotiate in exchanging for prolonging the person’s existence. It could be seen above as Jorgen says that he will only be good or in other words, accept his fate when he has visited Sweden.

Post your answer

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Which sentence from the essay best conveys the central idea of "Life Without Go Go Boots"? The rest of my life would be endurable if I had a pair of those white, calf-high confections with little black heels I learned what my mother had been trying to tell me all along: high fashion has the shelf life of potato salad. Style is mostly a matter of acting as if you know very well what you look like, thanks, and are just delighted about it I have a feeling the day might come when my daughter will beg to be a slave of conventional fashion.



Which sentence from the essay best conveys the central idea of “Life Without Go Go Boots”? The rest of my life would be endurable if I had a pair of those white, calf-high confections with little black heels I learned what my mother had been trying to tell me all along: high fashion has the shelf life of potato salad. Style is mostly a matter of acting as if you know very well what you look like, thanks, and are just delighted about it I have a feeling the day might come when my daughter will beg to be a slave of conventional fashion.

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John goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walks the rest of the way home. Which is the correct plot of total distance as a function of time for John’s jog?



John goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walks the rest of the way home. Which is the correct plot of total distance as a function of time for John’s jog?

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12] Which items might appear in a section in a textbook about medieval church power (2 answers) [A] Due process of the law [B] holy shrines [C] interdict [D] papal supremacy [E] pilgrimage [F] rule of law Anyone have the rest of the answers aswell?


I believe the answer is:

[C] interdict

[D] papal supremacy

Interdict refers to the rule that ban a certain individuals or members of the church to cite a passage or to follow a certain service in the church. Papal supremacy refers to the doctrine that acknowledge the pope of Vatican as figure with highest authority in the Christian Church.

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Emily is making a punch that contains 75% apple juice and the rest ginger ale. The punch has 2 liters of ginger ale. Part A: Write an equation using one variable that can be used to find the total number of liters of apple juice and ginger ale in the punch. Define the variable used in the equation. (5 points) Part B: How many liters of apple juice are present in the punch? Show your work. (5 points)



Emily is making a punch that contains 75% apple juice and the rest ginger ale. The punch has 2 liters of ginger ale. Part A: Write an equation using one variable that can be used to find the total number of liters of apple juice and ginger ale in the punch. Define the variable used in the equation. (5 points) Part B: How many liters of apple juice are present in the punch? Show your work. (5 points)

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The brain communicates with the rest of your body by _____.



The brain communicates with the rest of your body by _____.

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Suppose you have 30coins that total to $2.10 some of these coins are pennies and the rest are dimes which system of equations can be solved to find the number of each type of coin you have



Suppose you have 30coins that total to $2.10 some of these coins are pennies and the rest are dimes which system of equations can be solved to find the number of each type of coin you have

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What was one of the ways that the industrial revolution affected how the united states saw itself in relation to the rest of the world



What was one of the ways that the industrial revolution affected how the united states saw itself in relation to the rest of the world

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Which line best illustrates imagism? A. The pink sky sank into wet night. B. His mind remained clear but bereft of images. C. Yesterday lasted forever; tomorrow will never come. D. Those heroes of noble blood can sleep, but never can they rest.


The correct answer is
A. The pink sky sank into wet night

Imagism is about depicting vivid images usually by describing using vivid colors or things that are felt by senses. Presenting someone’s mind or concepts like yesterday and tomorrow is not imagism because it’s too abstract to imagine vividly. Same with the final sentence where it’s not very vivid.

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A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. what is its angular velocity (in rev/s) after a 22.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.


To answer this problem, we must remember that momentum is
conserved. Therefore,

Initial momentum = Final momentum

In this case we use angular momentum which it is defined
as:

Momentum =0.5 m ω^2

So finding for final angular velocity, ωf:

mi * ωi^2
= mf * ωf^2

120 kg * (0.5 rev / s)^2 = (120 kg + 22 kg) * ωf^2

ωf^2
= 0.2113

ωf = 0.46 rev/s

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In order to prevent injury during your weight-training session, it is necessary to __________. A. do performance testing prior to setting up your workout routine, stretch before and after each workout, get the proper amount of rest and nutrition, and modify your workout as needed B. have your friend check your workout to be sure it is well-designed, exercise only three days a week, and allow for adequate rest between workouts C. never change your workout routine, stretch before and after each workout, allow time to warm up and cool down, and adjust your form as needed D. use slow bouncing movements to warm up and stretch before each workout, follow a plan that includes proper sets and repetitions, adjust your workout and form as needed, and workout every day



In order to prevent injury during your weight-training session, it is necessary to __________. A. do performance testing prior to setting up your workout routine, stretch before and after each workout, get the proper amount of rest and nutrition, and modify your workout as needed B. have your friend check your workout to be sure it is well-designed, exercise only three days a week, and allow for adequate rest between workouts C. never change your workout routine, stretch before and after each workout, allow time to warm up and cool down, and adjust your form as needed D. use slow bouncing movements to warm up and stretch before each workout, follow a plan that includes proper sets and repetitions, adjust your workout and form as needed, and workout every day

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A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. the platform drops 6.00 cm before the person comes to rest. what is the spring constant of the spring?


Draw a diagram to illustrate the problem s shown in the figure below.

At state A, the person has potential energy relative to the spring of
PE = (60 kg)*(9.8 m/s²)*(1.2 m)
     = 705.6 J

At state B, the PE is converted to kinetic energy which is equal to the potential energy.
Assume that aerodynamic losses are ignored during the free fall.

At state C, the potential energy (or kinetic energy) is converted into strain energy in the spring. Assume that energy losses are negligible.
The spring deflects by  6 cm = 6×10⁻² m, and its spring constant = k N/m.
Therefore
(1/2)(k N/m)(6×10⁻² m)² = 705.6 J
k = 705.6/0.03 = 23520 N/m = 23.52 kN/m

Answer: 23.52 kN/m

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Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest. How much had Mrs. Ming invested in the account paying 6%?A.$117B.$680C.$760D.$820



Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest. How much had Mrs. Ming invested in the account paying 6%?A.$117B.$680C.$760D.$820

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Which response includes an opinion rather than just fact? Frida Kahlo’s passion for painting was so deep that it was the only thing that gave her joy. The bus accident caused Frida Kahlo to suffer from severe pain for the rest of her life. After the bus accident, Frida Kahlo abandoned her study of medicine to become a painter. Frida Kahlo’s artwork gained widespread recognition in the 1980s, many years after her death..


D. To move the reader toward the climax of the story This is the correct naswer.

Authors create tension to engage the readers. Tension is what makes a story  worth reading since it will touch or move the reader’s feelings. The reader’s rational side will be set aside by his/ her emotions.

These answers are not right:

A. To introduce the characters in the story and describe where the story takes place  ( This is part of the setting).

B. To reveal the author’s personal bias and opinion ( The opinion should be infered through the whole story , not jut through the tension in it).

C. To neatly tie up loose ends at the story’s close ( The tension leads to the climax not to the end of the story),

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If your are breathless and unable to talk normally during exercise,you should immediately A. Stop and notify your doctor B. Drink more water C. Go inside to rest D. Lower your exercise level


1. The answer is “C”.

“Identical twins” who have been raised apart are typically more similar in intelligence level than biological siblings raised together because they have been born with the same genetic code.

Identical twins originate from a single fertilized egg that parts into two. Before it parts, it is either male or female. After it parts, there are either two guys or two females. The two sections of the fertilized egg embed in the uterus and every create one of the twins.  

Identical twins have the equivalent hereditary source. No immediate reason for monozygotic twinning has been resolved; it isn’t innate. Monozygotic twins speak to around 33% all things considered. They may look strikingly comparative, and it might be hard to reveal to them separated.

2. The answer is “A”.

Lawrence Kohlberg felt that one of the only ways individuals will accomplish the objectives in each of his six stages was to participate in “consensus democracy” in small group settings.

Lawrence Kohlberg felt that the best way to support development through these stages was by discourse of good problems and by investment in consensus democracy inside small groups. Consensus democracy was rule by understanding of the gathering, not larger part rule. This would invigorate and widen the reasoning of youngsters and grown-ups, enabling them to advance starting with one phase then onto the next.

3. The answer is “D.  showing a learner how to correct common mistakes”.

The term scaffolding alludes to a procedure in which instructors display or exhibit how to take care of an issue, and afterward venture back, offering support as required. Analyst and instructional architect Jerome Bruner first utilized the term ‘scaffolding’ in this setting, harking back to the 1960s. The hypothesis is that when understudies are given the help they require while discovering some new information, they stand a superior possibility of utilizing that learning freely. Bruner suggests positive association and three methods of portrayal amid educating: activities, pictures, and dialect.  

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Block a, with a mass of 2.0kg, moves along the x axis with a velocity of 5.0m/s in the positive x direction. it su?ers an elastic collision with block b, initially at rest, and the blocks leave the collision along the x axis. if b is much more massive than a, the speed of a after the collision is:


The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies. 

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface. 

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h. 

So the time for the pencil and eraser to touch is T=1.3449 hours. 

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

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A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision…


Ahemmm having x-intercepts of -3 and -5.. ..well, that simply means, -3 and -5 are roots or solutions or zeros of the equation

it namely means x = -3 and x = -5, an x-intercept is when the graph touches the x-axis, at that point, the y-intercept is 0, so the point is (-3, 0) and (-5, 0)

if the roots are -3, and -5, then

bf begin{cases}
x=-3implies x+3=0implies &(x+3)=0\
x=-5implies x+5=0implies &(x+5)=0
end{cases}\\
-------------------------------\\
(x+3)(x+5)=0implies (x+3)(x+5)=yimplies x^2+8x+15=y

if you have the zeros/x-intercepts/solutions of the polynomial, all you have to do is, get the factors, as above, and get their product, to get the parent original polynomial.

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Things did not go quite as planned. you invested $20,000, part of it in a fund that paid 12% annual interest. however, the rest of the money suffered a 5% loss. if the total annual income from both investments was $1890, how much was invested at each rate?


Initial investment on Jan 1, 2013 = (500 shares)*($24 per share) = $12,000

Dividend collected at the end of 2013 = $2.50*500 = $1,250
Dividend collected at the end of 2014 = $4*500 = $2,000
Dividend collected at the end of 2015 = $3*500 = $1,500
Mony received from sellng the 500 shares at the end of 2015 = $20*500 = $10,000

Total returns at the end of 2015 = 1,250+2,000+1,500+10,000 = $14,750
Net gains = 14750 – 12000 = $2,750
Duration = 3 years
Realized total rate of return = 2750/12000 = 0.2292 = 22.9%

Answer: 22.9%

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A ball of mass 0.5 kg is released from rest at a height of 30 m. How fast is it going when it hits the ground? Acceleration due to gravity is g = 9.8 m/s²


Answer:

1) Water has very high specific heat.

2) It expands when it freezes

3) ability to dissolve in ionic substances

4) Water molecules at the surface experience fewer hydrogen bonds than water molecules within the liquid.

Explanation:

1) Water molecules due to their high specific heat , undergo relatively less increase in temperature after absorbing heat. So they prevent their adjoining area to experience sharp increase in temperature.

2) Water is an example which expands on freezing. In it , large spaces are left between molecules when it cools. It happens because hydrogen bonds prevent any two molecules to come very close thereby  creating gaps. This gap is filled up when ice melts , which results in overall reduction in volume of water.

3) Uneven distribution of charge results in water molecules becoming polar in nature . A polar substance  can be dissolved in polar solvents only.

4) It is due to property of surface tension. Property  of surface tension results due to molecules of water near the surface experiencing a  net downward  force due to hydrogen bonds . It is due to fewer hydrogen bonds made by them.

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Kim is taking part in a group discussion about the book they are reading for class. She quickly becomes aware that the rest of the group did not prepare for this discussion. Which action is a definite sign that the group did not prepare? A. They keep flipping the pages of their books, looking for something to say. B. They seem to be very comfortable reading aloud from the textbook. C. They have chosen a section of the book that they think is important to discuss. D. They are confident when the moderator brings up a topic to discuss. 100 POINT easy question easy answer please help me


Hey there!

Correct answer is D. Comma or Period Inside Rule

A. Question mark or exclamation point inside: those are not really necessary.

B. Colon or semicolon: not, a semicolon would divide the whole sentence and it would be shorten; a colon would work but after requested, when there is already a comma.

C. Question mark or Exclamation Point Outside Rule: would not work, becase it is an very polite and affirmative sentence.

D: A comma or period inside rule: actually, just a comma would work. Please, Cooper’s dad requested, go… Cooper’s dad requested must be in between commas as it is a vocative.

Hope this helps

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Read the excerpt from The Code Book. More than a hundred million e-mails are sent around the world each day, and they are all vulnerable to interception. Digital technology has aided communication, but it has also given rise to the possibility of those communications being monitored. According to Zimmermann, cryptographers have a duty to encourage the use of encryption and thereby protect the privacy of the individual: A future government could inherit a technology infrastructure that’s optimized for surveillance, where they can watch the movements of their political opposition, every financial transaction, every communication, every bit of e-mail, every phone call. Everything could be filtered and scanned and automatically recognized by voice recognition technology and transcribed. It’s time for cryptography to step out of the shadows of spies and the military, and step into the sunshine and be embraced by the rest of us. In the excerpt, the purpose of the statistic “more than a hundred million e-mails” is to show that digital information is widespread and available to monitoring. most e-mails that are sent are not viewed by the government. encryption has been used by the military but not ordinary citizens. e-mail is a good way for people to communicate nowadays.


Answer:

Gather references, and prepare your résumé.

Explanation:

Before a job interview, it is advisable to prepare a copy of your résumé and references, as well as bring a pen and notepad.

The rest of the alternatives are incorrect because asking the company to keep your résumé on file is inappropriate – you should always carry a copy of  it; asking and answering questions politely happens during the course of the interview; and restating your interest is done after the interview has occurred.

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Compared to the rest of Europe, vacations in Eastern Europe have been substantially overpriced. True False


Natural Forces Affecting the Driver:

1. While the car stops, the person continues moving the way that the car were moving and then hits the obstacle in the car or the person can be thrown out of the vehicle. If the person wears belt, he will stop moving with the vehicle and won’t hit the obstacle.

2. We count approximate kinetic energy using the formula K = v^2. So the vehicle which is moving at 30 mph will have four times less kinetic energy than vehicle which is moving at 60 mph. If they have the same road conditions, the breaking distance will be four times as great for the car moving twice as fast.

3. Kinetic energy depends on object’s mass and velocity and it has direct relationship with the stopping distance. The lesser mass of the vehicle = the lesser kinetic energy and lesser stopping distance. => If both vehicles have the same velocity, then small vehicle has lesser kinetic energy than large vehicle.

4. We know that kinetic energy has this relationship with velocity K = v^2. So the best way to prepare to enter sharp curves in the roadway is to lower the speed. The most appropriate speed is 20-30 mph, but it depends on road conditions and car’s breaks condition.

5. Car crashes can happen with everyone so the best way is to be prepared. First the driver should wear a seatbelt while he’s driving. He should check his tires and breaks condition regularly. And also it’s important to slow down the vehicle while entering sharp curves. Without following these rules, the driver can get catastrophic injuries in a car crash.

Signs, Signals, and Pavement Markings: 

1. It doesn’t matter where you go. All you need is to learn highway code. It’s very different to know the meanings of every road sign. Also, it’s necessary to check your car’s conditions and you should take some spare parts for your car in case of accidents. So wherever you go, it’s important to be prepared.

2. You should stop before crossing and take few minutes to make sure there is no train approaching. If there is no train approaching, you can pass a railroad crossing. If you see approaching train, you should wait until it will pass a railroad crossing.

3. You should stop before the lights and wait to check the traffic movement and signs. Make sure that everything is safe and pass the intersection. Don’t move fast to avoid accidents.

4. Flashing yellow light means that it’s not necessary to stop but you should to pay attention on the traffic movement. So it would be better to yield before the lights and make sure if it’s safe to move. After that you can cross the intersection.

5. The line change means that the lane changes and you can’t cross solid lines. Pay more attention on road marking because it shows how you should behave on the road or highway.

6. As you approach the next exit and  your passengers need to use the restroom and get some food, you should look for green signs which indicate food and rest stops. You should to slow down if you don’t want to skip the sign.

7. When you take the exit ramp off the expressway and merge onto the next road, you see yellow lines dividing the roadway which indicates that there is oncoming traffic and this is a two-way highway. 

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Josh kept 75% of the ride tickets he bought at a carnival and gave the rest to his friend Sam. Sam gave 50% of these tickets to Rob. If Rob was given 3 tickets, how many tickets did Josh buy?


Solution:

The Given Rectangle having dimensions

Length = 80 cm

Breadth = 50 cm

Let the Six squares which has been cut from this rectangle have side of length a cm.

Area of each square = (Side)²= a²

Area of 6 Identical Squares = 6 × a²= 6 a²

If four squares are cut from four corners and two along Length,

then , Length of Box = (80 – 3 a)cm, Breadth of Box = (50 – 2 a)cm, Height = a cm

Volume of Box =V = Length × Breadth × Height

    V = (80 – 3 a)× (50 – 2 a)× a

     V   = 4000 a – 310 a² + 6 a³

For Maximum Volume

V’= 0 , where V’ = Derivative of V with respect to a.

V’= 4000 – 620 a + 18 a²

V’ =0

18 a² – 620 a + 4000= 0

9 a² – 310 a + 2000=0

using determinant method

a = frac{310pmsqrt{96100-72000}}{18}=frac{310pm155}{18}=frac{310-155}{18}=8.6 cm

V”=1 8 a – 310 = -ve

which shows , when a = 8.6 cm , volume is maximum.

So, V = 4000×8.6 – 310×(8.6)²+6×(8.6)³=15288.736 cm³

OR

If four squares are cut from four corners and two along Breadth,

then , Length of Box = (80 – 2 a)cm, Breadth of Box = (50 –  3 a)cm, Height = a cm

Volume of Box =V = Length × Breadth × Height

    V = (80 – 2 a)× (50 – 3 a)× a

     V   = 4000 a – 340 a² + 6 a³

For Maximum Volume

V’= 0 , where V’ = Derivative of V with respect to a.

V’= 4000 – 680 a + 18 a²

V’ =0

18 a² – 680 a + 4000= 0

9 a² – 340 a + 2000=0

Using Determinant method

a = frac{340pmsqrt{115600-72000}}{18}=frac{340pm209}{18}=frac{131}{18}=7.6 cm

V”=18 a -340= -ve value when a = 7.6 cm, shows volume is maximum when a = 7.6 cm

V= 4000×7.6 -340 × (7.6)² +6× (7.6)³=13395.456 cubic cm